Textbook Question
5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. How much heat energy is transferred to the gas to cause this expansion?
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Ch 19: Work, Heat, and the First Law of Thermodynamics
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
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Knight Calc 5th EditionCh 19: Work, Heat, and the First Law of ThermodynamicsProblem 56c
Knight Calc 5th EditionCh 19: Work, Heat, and the First Law of ThermodynamicsProblem 56cChapter 19, Problem 56c
n moles of an ideal gas at temperature T1 and volume V1 expand isothermally until the volume has doubled. In terms of n, T1, and V1, what are the heat energy transferred to the gas?
Verified step by step guidance1
Step 1: Recognize that the process is isothermal, meaning the temperature (T₁) remains constant throughout the expansion. For an ideal gas undergoing an isothermal process, the internal energy change (ΔU) is zero because internal energy depends only on temperature for an ideal gas.
Step 2: Recall the first law of thermodynamics: ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat energy transferred to the gas, and W is the work done by the gas. Since ΔU = 0 for an isothermal process, we have Q = W.
Step 3: The work done by the gas during an isothermal expansion can be calculated using the formula: W = nRT₁ ln(V₂/V₁), where n is the number of moles, R is the ideal gas constant, T₁ is the constant temperature, and V₂ and V₁ are the final and initial volumes, respectively.
Step 4: Substitute the given condition that the volume doubles, so V₂ = 2V₁. The work done becomes: W = nRT₁ ln(2). Since Q = W, the heat energy transferred to the gas is also Q = nRT₁ ln(2).
Step 5: Conclude that the heat energy transferred to the gas during the isothermal expansion is Q = nRT₁ ln(2). This result is expressed in terms of the given variables n, T₁, and V₁, and does not depend on the specific value of V₁ because it cancels out in the logarithmic ratio.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Ideal Gas Law
The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of an ideal gas through the equation PV = nRT. This law is fundamental in understanding the behavior of gases under various conditions, including isothermal processes where temperature remains constant.
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Ideal Gases and the Ideal Gas Law
Isothermal Process
An isothermal process is a thermodynamic process that occurs at a constant temperature. For an ideal gas, during isothermal expansion, the internal energy remains unchanged, and any work done by the gas is compensated by heat absorbed from the surroundings, which is crucial for calculating heat transfer.
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First Law of Thermodynamics
The First Law of Thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In the context of isothermal expansion, this principle helps determine the heat energy transferred to the gas, as the work done during expansion must equal the heat absorbed.
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Related Practice
Textbook Question
n moles of an ideal gas at temperature T1 and volume V1 expand isothermally until the volume has doubled. In terms of n, T1, and V1, what is the final temperature?
1
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Textbook Question
5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. What are the gas volume and temperature after the expansion?
1
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Textbook Question
5.0 g of nitrogen gas at 20°C and an initial pressure of 3.0 atm undergo an isobaric expansion until the volume has tripled. What is the gas pressure after the decrease?
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Textbook Question
n moles of an ideal gas at temperature T1 and volume V1 expand isothermally until the volume has doubled. In terms of n, T1, and V1, what are the work done on the gas?
1
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Textbook Question
A 10-cm-diameter cylinder contains argon gas at 10 atm pressure and a temperature of 50°C. A piston can slide in and out of the cylinder. The cylinder's initial length is 20 cm. 2500 J of heat are transferred to the gas, causing the gas to expand at constant pressure. What are the final length of the cylinder?